Good morning, i'm hoping someone will be able to help me out. I have set up a linear regression array in Excel and now want to test the significance of my r2 value at a certain level of significance. I've only been able to find tables that give the critical r value, but I want to test it at 99.73% level of confidence and none of them contain that specific value. Is there a way to do this in Excel? Thank you for your help!
r is basically tested for significance with null hypotesis that ro is 0. Then statistics:
r*sqrt(n-2)/(1-r^2)
is calculated
and if this statistics fall into (-inf,-q) or (q,+inf) then null hypotesis shall be rejected
the 1-(alfa/2) quantile q of t-Student distribution of n-2 degrees of freedom could be found from from excel function.
as you need 99.73% level of confidence (very high indeed - have you considered a smaller one, because with so high confidence level you are quite prone to second type errors) so alfa = 0.27% you will get the quantile q from:
=TINV(0.27%,n-2)
(of course instead of n-2 write your number of XY pairs decreased by 2)
Best Regards,
Kaper
Thank you for getting back to me! So let me see if i'm on the right track here. Let's say for example I'm working with 5 calibrators so my n-2=3. From =TINV(0.27, 3) I get back 1.35.
I then compare that value to the value I get from putting my r^2 value into the equation that you provided and if it falls outside of the TINV value, there is a significant linear relationship?
1) =TINV(0.27%,3)
2) yes is significant in "normal words" but as it is testing statistical hypotesis, basicallay you just say, you reject hypotesis of lack of correlation at 99.73% confidence level (0.27% or 0.0027significance level)
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